HOLLYWOOD, Florida (CNN) -- A deceased drifter long suspected in the abduction, murder and beheading of 6-year-old Adam Walsh committed the crime that put missing children on the national agenda, police said Tuesday.

Adam Walsh 6, disappeared from a mall in August, 1981. His head was found two weeks later, 120 miles away.

"If Ottis Toole was alive today, he would be arrested for the abduction and murder of Adam Walsh on July 27, 1981," Hollywood Police Chief Chad Wagner said at an afternoon news conference announcing the end of the 27-year investigation.

The chief apologized to the boy's parents, John and Reve Walsh, for what he called "lapses" in the initial investigation.

He added that there was no "magic" piece of evidence that led investigators to officially name a suspect now.

"This case could have been closed, and should have been closed years ago," Wagner said.

When he took over last year as police chief, Wagner vowed to close the Walsh case.

John Walsh's voice shook and his eyes brimmed with tears as he thanked the chief for closing the case. Walsh is best known as host of the television show "America's Most Wanted." Watch Walsh's reaction »

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"For 27 years, we have been asking ourselves, 'Who would take a 6-year-old boy and murder him and decapitate him? Who? ' " Walsh said. "We needed to know. Today we know. The not knowing has been a torture but now that journey is over. It is only fitting that it ends here at this police department." Watch Reve Walsh thank her children »

Toole, a convicted pedophile and killer who associated with notorious serial killer Henry Lee Lucas, died in prison in 1996. Wagner said investigators were able to place Toole in Hollywood at the time Adam disappeared.

Toole twice confessed to killing the boy -- and twice recanted his story, saying he made it up. It could not be learned what, if any, new evidence exists.

Adam disappeared from a Sears store across from the Hollywood police station in July 1981. Two weeks later, his severed head was found in a canal 120 miles away. The boy's body was never recovered, and no one was ever charged in the case.

Walsh turned his grief into action, becoming an early advocate for missing children and crime victims. Three presidents -- Ronald Reagan, George H.W. Bush and Bill Clinton -- have honored Walsh for his efforts to safeguard children.

His efforts led to the passage of the federal Missing Children's Assistance Act of 1984, which established the National Center for Missing and Exploited Children.

His fierce loathing of fugitives, convicts and predators launched a new career as host of the television show "America's Most Wanted."

Walsh has long believed Toole killed Adam, and on Tuesday, Wagner said there never was any other suspect. Toole died in prison in 1996 while serving a life sentence on unrelated charges.

Toole's confessions in the Walsh case were questioned by police because Toole confessed to other murders that police knew he did not commit.

Although the details of his story changed, Toole did lead police to the Sears store and pointed out the spot where Adam was last seen. He also led police to the canal where the boy's head was found.

But investigators could not find Adam's body where Toole said he left it.

A bloody piece of carpet removed from Toole's car was lost by police many years ago, before DNA testing became available.

Police believe a 17-year-old security guard asked a handful of rowdy kids who were playing video games in the toy department to leave the store. Investigators believe Adam was grouped in with those kids, who left him alone outside the store. That was the last time he was seen.